Improved measurement of the branching fraction and energy spectrum of ${\eta }^{\prime }$ from ${\rm Y}(1S)$ decays

We present an improved measurement of the ${\eta }^{\prime }$ meson energy spectrum in ${\rm Y}(1S)$ decays, using $1.2{\mathrm{fb}}^{-1}$ of data taken at the ${\rm Y}(1S)$ center-of-mass energy with the CLEO III detector. We compare our results with models of the ${\eta }^{\prime }$ gluonic form factor that have been suggested to explain the unexpectedly large $B\to {\eta }^{\prime }{X}_s$ rate. Models based on perturbative QCD fail to fit the data for large ${\eta }^{\prime }$ energies, and thus an explanation outside the realm of the Standard Model or an improved understanding of nonperturbative QCD effects may be needed to account for this large rate.

Figure 1

Feynman Diagram for $b\to s(g^{\star }\to g{\eta }^{\prime })$ (left) and ${\rm Y}(1S)\to gg{g}^{\star }\to {\eta }^{\prime }X$ (right).

Figure 2

The spectra of the difference of the $\eta {\pi }^{+}{\pi }^{-}$ and $\eta$ invariant masses in different $Z$ ranges reconstructed from ${\rm Y}(1S)$ data, fit with a single Gaussian function for the signal and a first-order polynomial for the background.

Figure 3

The spectra of the difference of the $\eta {\pi }^{+}{\pi }^{-}$ and $\eta$ invariant masses in different $Z$ ranges reconstructed from continuum data taken at a center-of-mass energy of 10.54 GeV, fit with a single Gaussian function for the signal and a first-order polynomial for the background.

Figure 4

The ${\eta }^{\prime }$ reconstruction efficiencies as function of $Z$ for different MC samples with no ${\pi }^0$ veto, and with ${\pi }^0$ veto in photon selection. The ${\pi }^0$ veto was applied in this analysis for $Z<0.5$.

Figure 5

The measured differential cross sections $d{\sigma }_{{\eta }^{\prime }}/dZ$ for (a) ${\gamma }^{\star }\to q\overline{q}\to {\eta }^{\prime }X$ (shaded), (b) ${\rm Y}(1S)\to q\overline{q}\to {\eta }^{\prime }X$ (white) and (c) ${\rm Y}(1S)\to gg{g}^{\star }\to {\eta }^{\prime }X$ (black).

Figure 6

The energy distribution function $dn/dZ$ as defined in the text for (a) ${\rm Y}(1S)\to gg{g}^{\star }\to {\eta }^{\prime }X$, (b) ${\rm Y}(1S)\to q\overline{q}\to {\eta }^{\prime }X$, and (c) ${\rm Y}(1S)\to {\eta }^{\prime }X$.

Figure 7

Energy spectrum of the ${\eta }^{\prime }$-meson in the decay ${\rm Y}(1S)\to {\eta }^{\prime }X$ (open squares correspond to the data presented in this paper, filled circles are the previously reported CLEO II data [13]): (a) measured spectra (log scale); (b) expanded view of the $Z\ge 0.7$ region to show the comparison with the theoretical predictions more clearly (linear scale). The dashed curve corresponds to a constant value of the function $H(p^2)=H_0\simeq 1.7{\mathrm{GeV}}^{-1}$, and the dash-dotted curve ($H_{\mathrm{as}}(p^2)$) corresponds to the asymptotic form of the ${\eta }^{\prime }$-meson LCDA [14] (i.e., $B_2^{(q)}=0$ and $B_2^{(g)}=0$). The spectrum with the Gegenbauer coefficients [14] in the combined best-fit range of these parameters is shown in the shaded region. The solid curve corresponds to the best-fit values of the parameters in the form factors from Ref. [14] from the analysis of the ${\rm Y}(1S)\to {\eta }^{\prime }X$ CLEO II data alone.